Using adaptive mesh refinement simulations I will describe the evolution of the magnetic field in the hot plasma of a galaxy cluster. I will point out that this field is more amplified in the cluster core if the cluster experienced a cooling flow than in a pure adiabatic case. But this scenario becomes even more complex when an active galactic nuclei releases energy into the intra-cluster medium and leads to the destruction of the cool core of the cluster. The initial seed field, which is a free parameter in these models, is chosen to produce results in agreement with observations. But the origin of the cosmological magnetic field is still uncertain. Expanding galactic winds due to supernovae feedback can provide a coherent scenario of the magnetic enrichment of the inter-galactic medium, and then draw a new scenario on the origin of the magnetic field at very large scales.